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Shared Qs (012)


  1. Question

    A list of inputs and outputs is expressed as \((x,y)\) pairs.

    ( 8 , 2 )

    ( 7 , 4 )

    ( 1 , 3 )

    ( 5 , 6 )

    ( 2 , 5 )

    ( 6 , 2 )

    ( 6 , 7 )

    Is this list consistent with \(y\) being a function of \(x\)?

    Is this list consistent with \(x\) being a function of \(y\)?

    Is this list consistent with a one-to-one function?



    Solution


  2. Question

    A list of inputs and outputs is expressed as \((x,y)\) pairs.

    ( 1 , 3 )

    ( 4 , 1 )

    ( 2 , 9 )

    ( 5 , 4 )

    ( 6 , 5 )

    ( 6 , 5 )

    Is this list consistent with \(y\) being a function of \(x\)?

    Is this list consistent with \(x\) being a function of \(y\)?

    Is this list consistent with a one-to-one function?



    Solution


  3. Question

    A list of inputs and outputs is expressed as \((x,y)\) pairs.

    ( 8 , 7 )

    ( 4 , 5 )

    ( 3 , 3 )

    ( 4 , 5 )

    ( 1 , 5 )

    Is this list consistent with \(y\) being a function of \(x\)?

    Is this list consistent with \(x\) being a function of \(y\)?

    Is this list consistent with a one-to-one function?



    Solution


  4. Question

    A list of inputs and outputs is expressed as \((x,y)\) pairs.

    ( 5 , 1 )

    ( 6 , 8 )

    ( 3 , 4 )

    ( 1 , 4 )

    ( 1 , 4 )

    Is this list consistent with \(y\) being a function of \(x\)?

    Is this list consistent with \(x\) being a function of \(y\)?

    Is this list consistent with a one-to-one function?



    Solution


  5. Question

    A list of inputs and outputs is expressed as \((x,y)\) pairs.

    ( 9 , 4 )

    ( 6 , 5 )

    ( 6 , 5 )

    ( 9 , 4 )

    ( 4 , 2 )

    Is this list consistent with \(y\) being a function of \(x\)?

    Is this list consistent with \(x\) being a function of \(y\)?

    Is this list consistent with a one-to-one function?



    Solution


  6. Question

    A list of inputs and outputs is expressed as \((x,y)\) pairs.

    ( 4 , 7 )

    ( 9 , 9 )

    ( 5 , 8 )

    ( 7 , 3 )

    ( 8 , 5 )

    ( 2 , 1 )

    ( 5 , 8 )

    Is this list consistent with \(y\) being a function of \(x\)?

    Is this list consistent with \(x\) being a function of \(y\)?

    Is this list consistent with a one-to-one function?



    Solution


  7. Question

    A list of inputs and outputs is expressed as \((x,y)\) pairs.

    ( 3 , 2 )

    ( 5 , 6 )

    ( 2 , 4 )

    ( 4 , 9 )

    ( 8 , 3 )

    ( 8 , 3 )

    Is this list consistent with \(y\) being a function of \(x\)?

    Is this list consistent with \(x\) being a function of \(y\)?

    Is this list consistent with a one-to-one function?



    Solution


  8. Question

    A list of inputs and outputs is expressed as \((x,y)\) pairs.

    ( 5 , 4 )

    ( 2 , 1 )

    ( 6 , 6 )

    ( 6 , 4 )

    ( 8 , 8 )

    ( 8 , 7 )

    Is this list consistent with \(y\) being a function of \(x\)?

    Is this list consistent with \(x\) being a function of \(y\)?

    Is this list consistent with a one-to-one function?



    Solution


  9. Question

    A list of inputs and outputs is expressed as \((x,y)\) pairs.

    ( 7 , 3 )

    ( 3 , 8 )

    ( 5 , 6 )

    ( 1 , 6 )

    ( 1 , 9 )

    Is this list consistent with \(y\) being a function of \(x\)?

    Is this list consistent with \(x\) being a function of \(y\)?

    Is this list consistent with a one-to-one function?



    Solution


  10. Question

    A list of inputs and outputs is expressed as \((x,y)\) pairs.

    ( 3 , 3 )

    ( 8 , 7 )

    ( 1 , 9 )

    ( 4 , 5 )

    ( 1 , 9 )

    ( 7 , 6 )

    ( 1 , 9 )

    Is this list consistent with \(y\) being a function of \(x\)?

    Is this list consistent with \(x\) being a function of \(y\)?

    Is this list consistent with a one-to-one function?



    Solution


  11. Question

    plot of chunk unnamed-chunk-1

    Are these points consistent with \(y\) being a function of \(x\)?

    Are these points consistent with \(x\) being a function of \(y\)?

    Are these points consistent with a one-to-one function?



    Solution


  12. Question

    plot of chunk unnamed-chunk-1

    Are these points consistent with \(y\) being a function of \(x\)?

    Are these points consistent with \(x\) being a function of \(y\)?

    Are these points consistent with a one-to-one function?



    Solution


  13. Question

    plot of chunk unnamed-chunk-1

    Are these points consistent with \(y\) being a function of \(x\)?

    Are these points consistent with \(x\) being a function of \(y\)?

    Are these points consistent with a one-to-one function?



    Solution


  14. Question

    plot of chunk unnamed-chunk-1

    Are these points consistent with \(y\) being a function of \(x\)?

    Are these points consistent with \(x\) being a function of \(y\)?

    Are these points consistent with a one-to-one function?



    Solution


  15. Question

    plot of chunk unnamed-chunk-1

    Are these points consistent with \(y\) being a function of \(x\)?

    Are these points consistent with \(x\) being a function of \(y\)?

    Are these points consistent with a one-to-one function?



    Solution


  16. Question

    plot of chunk unnamed-chunk-1

    Are these points consistent with \(y\) being a function of \(x\)?

    Are these points consistent with \(x\) being a function of \(y\)?

    Are these points consistent with a one-to-one function?



    Solution


  17. Question

    plot of chunk unnamed-chunk-1

    Are these points consistent with \(y\) being a function of \(x\)?

    Are these points consistent with \(x\) being a function of \(y\)?

    Are these points consistent with a one-to-one function?



    Solution


  18. Question

    plot of chunk unnamed-chunk-1

    Are these points consistent with \(y\) being a function of \(x\)?

    Are these points consistent with \(x\) being a function of \(y\)?

    Are these points consistent with a one-to-one function?



    Solution


  19. Question

    plot of chunk unnamed-chunk-1

    Are these points consistent with \(y\) being a function of \(x\)?

    Are these points consistent with \(x\) being a function of \(y\)?

    Are these points consistent with a one-to-one function?



    Solution


  20. Question

    plot of chunk unnamed-chunk-1

    Are these points consistent with \(y\) being a function of \(x\)?

    Are these points consistent with \(x\) being a function of \(y\)?

    Are these points consistent with a one-to-one function?



    Solution


  21. Question

    plot of chunk unnamed-chunk-1

    Are these connections consistent with \(y\) being a function of \(x\)?

    Are these connections consistent with \(x\) being a function of \(y\)?

    Are these connections consistent with a one-to-one function?



    Solution


  22. Question

    plot of chunk unnamed-chunk-1

    Are these connections consistent with \(y\) being a function of \(x\)?

    Are these connections consistent with \(x\) being a function of \(y\)?

    Are these connections consistent with a one-to-one function?



    Solution


  23. Question

    plot of chunk unnamed-chunk-1

    Are these connections consistent with \(y\) being a function of \(x\)?

    Are these connections consistent with \(x\) being a function of \(y\)?

    Are these connections consistent with a one-to-one function?



    Solution


  24. Question

    plot of chunk unnamed-chunk-1

    Are these connections consistent with \(y\) being a function of \(x\)?

    Are these connections consistent with \(x\) being a function of \(y\)?

    Are these connections consistent with a one-to-one function?



    Solution


  25. Question

    plot of chunk unnamed-chunk-1

    Are these connections consistent with \(y\) being a function of \(x\)?

    Are these connections consistent with \(x\) being a function of \(y\)?

    Are these connections consistent with a one-to-one function?



    Solution


  26. Question

    plot of chunk unnamed-chunk-1

    Are these connections consistent with \(y\) being a function of \(x\)?

    Are these connections consistent with \(x\) being a function of \(y\)?

    Are these connections consistent with a one-to-one function?



    Solution


  27. Question

    plot of chunk unnamed-chunk-1

    Are these connections consistent with \(y\) being a function of \(x\)?

    Are these connections consistent with \(x\) being a function of \(y\)?

    Are these connections consistent with a one-to-one function?



    Solution


  28. Question

    plot of chunk unnamed-chunk-1

    Are these connections consistent with \(y\) being a function of \(x\)?

    Are these connections consistent with \(x\) being a function of \(y\)?

    Are these connections consistent with a one-to-one function?



    Solution


  29. Question

    plot of chunk unnamed-chunk-1

    Are these connections consistent with \(y\) being a function of \(x\)?

    Are these connections consistent with \(x\) being a function of \(y\)?

    Are these connections consistent with a one-to-one function?



    Solution


  30. Question

    plot of chunk unnamed-chunk-1

    Are these connections consistent with \(y\) being a function of \(x\)?

    Are these connections consistent with \(x\) being a function of \(y\)?

    Are these connections consistent with a one-to-one function?



    Solution


  31. Question

    plot of chunk unnamed-chunk-1

    Is this curve consistent with \(y\) being a function of \(x\)?

    Is this curve consistent with \(x\) being a function of \(y\)?

    Is this curve consistent with a one-to-one function?



    Solution


  32. Question

    plot of chunk unnamed-chunk-1

    Is this curve consistent with \(y\) being a function of \(x\)?

    Is this curve consistent with \(x\) being a function of \(y\)?

    Is this curve consistent with a one-to-one function?



    Solution


  33. Question

    plot of chunk unnamed-chunk-1

    Is this curve consistent with \(y\) being a function of \(x\)?

    Is this curve consistent with \(x\) being a function of \(y\)?

    Is this curve consistent with a one-to-one function?



    Solution


  34. Question

    plot of chunk unnamed-chunk-1

    Is this curve consistent with \(y\) being a function of \(x\)?

    Is this curve consistent with \(x\) being a function of \(y\)?

    Is this curve consistent with a one-to-one function?



    Solution


  35. Question

    plot of chunk unnamed-chunk-1

    Is this curve consistent with \(y\) being a function of \(x\)?

    Is this curve consistent with \(x\) being a function of \(y\)?

    Is this curve consistent with a one-to-one function?



    Solution


  36. Question

    plot of chunk unnamed-chunk-1

    Is this curve consistent with \(y\) being a function of \(x\)?

    Is this curve consistent with \(x\) being a function of \(y\)?

    Is this curve consistent with a one-to-one function?



    Solution


  37. Question

    plot of chunk unnamed-chunk-1

    Is this curve consistent with \(y\) being a function of \(x\)?

    Is this curve consistent with \(x\) being a function of \(y\)?

    Is this curve consistent with a one-to-one function?



    Solution


  38. Question

    plot of chunk unnamed-chunk-1

    Is this curve consistent with \(y\) being a function of \(x\)?

    Is this curve consistent with \(x\) being a function of \(y\)?

    Is this curve consistent with a one-to-one function?



    Solution


  39. Question

    plot of chunk unnamed-chunk-1

    Is this curve consistent with \(y\) being a function of \(x\)?

    Is this curve consistent with \(x\) being a function of \(y\)?

    Is this curve consistent with a one-to-one function?



    Solution


  40. Question

    plot of chunk unnamed-chunk-1

    Is this curve consistent with \(y\) being a function of \(x\)?

    Is this curve consistent with \(x\) being a function of \(y\)?

    Is this curve consistent with a one-to-one function?



    Solution


  41. Question

    Let function \(f\) be defined as follows: \[f(x) = 2 x^{2} + 5 x + 4\] Evaluate \(f(6.11)\).

    You can round (or truncate) at the tenths place.


    Solution


  42. Question

    Let function \(f\) be defined as follows: \[f(x) = - 4 x^{2} + 4 x + 3\] Evaluate \(f(-3.29)\).

    You can round (or truncate) at the tenths place.


    Solution


  43. Question

    Let function \(f\) be defined as follows: \[f(x) = - 2 x^{2} - 5 x - 3\] Evaluate \(f(-6.6)\).

    You can round (or truncate) at the tenths place.


    Solution


  44. Question

    Let function \(f\) be defined as follows: \[f(x) = - 2 x^{2} + 3 x + 5\] Evaluate \(f(0.24)\).

    You can round (or truncate) at the tenths place.


    Solution


  45. Question

    Let function \(f\) be defined as follows: \[f(x) = 3 x^{2} + 4 x - 5\] Evaluate \(f(-7.27)\).

    You can round (or truncate) at the tenths place.


    Solution


  46. Question

    Let function \(f\) be defined as follows: \[f(x) = - 5 x^{2} - 2 x - 3\] Evaluate \(f(-0.56)\).

    You can round (or truncate) at the tenths place.


    Solution


  47. Question

    Let function \(f\) be defined as follows: \[f(x) = - 2 x^{2} + 2 x + 4\] Evaluate \(f(9.08)\).

    You can round (or truncate) at the tenths place.


    Solution


  48. Question

    Let function \(f\) be defined as follows: \[f(x) = - 3 x^{2} - 5 x + 5\] Evaluate \(f(2.29)\).

    You can round (or truncate) at the tenths place.


    Solution


  49. Question

    Let function \(f\) be defined as follows: \[f(x) = - 3 x^{2} - 2 x + 4\] Evaluate \(f(-1.82)\).

    You can round (or truncate) at the tenths place.


    Solution


  50. Question

    Let function \(f\) be defined as follows: \[f(x) = 5 x^{2} + 4 x - 3\] Evaluate \(f(4.18)\).

    You can round (or truncate) at the tenths place.


    Solution


  51. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  52. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  53. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  54. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  55. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  56. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  57. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  58. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  59. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  60. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  61. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  62. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  63. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  64. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  65. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  66. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  67. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  68. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  69. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  70. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1


    Solution


  71. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 5 x^{3} + 5 x^{2} - 2 x + 4\] Which of the following expressions is equivalent to \(f(-a)\)?


    1. \(5 a^{3} + 5 a^{2} + 2 a + 4\)
    2. \(5 a^{3} - 5 a^{2} + 2 a - 4\)
    3. \(- 5 a^{3} + 5 a^{2} - 2 a + 4\)
    4. \(- 5 a^{3} - 5 a^{2} - 2 a - 4\)

    Solution


  72. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 2 x^{3} + 4 x^{2} - 2 x + 5\] Which of the following expressions is equivalent to \(f(-a)\)?


    1. \(- 2 a^{3} + 4 a^{2} + 2 a + 5\)
    2. \(2 a^{3} - 4 a^{2} - 2 a - 5\)
    3. \(- 2 a^{3} - 4 a^{2} + 2 a - 5\)
    4. \(2 a^{3} + 4 a^{2} - 2 a + 5\)

    Solution


  73. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 3 x^{3} + 4 x^{2} + 5 x + 3\] Which of the following expressions is equivalent to \(f(-a)\)?


    1. \(3 a^{3} - 4 a^{2} - 5 a - 3\)
    2. \(3 a^{3} + 4 a^{2} - 5 a + 3\)
    3. \(- 3 a^{3} - 4 a^{2} + 5 a - 3\)
    4. \(- 3 a^{3} + 4 a^{2} + 5 a + 3\)

    Solution


  74. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 2 x^{3} + 5 x^{2} + 3 x + 2\] Which of the following expressions is equivalent to \(f(-a)\)?


    1. \(- 2 a^{3} + 5 a^{2} + 3 a + 2\)
    2. \(2 a^{3} + 5 a^{2} - 3 a + 2\)
    3. \(2 a^{3} - 5 a^{2} - 3 a - 2\)
    4. \(- 2 a^{3} - 5 a^{2} + 3 a - 2\)

    Solution


  75. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 2 x^{3} - 3 x^{2} - 4 x - 5\] Which of the following expressions is equivalent to \(f(-a)\)?


    1. \(2 a^{3} - 3 a^{2} + 4 a - 5\)
    2. \(- 2 a^{3} - 3 a^{2} - 4 a - 5\)
    3. \(2 a^{3} + 3 a^{2} + 4 a + 5\)
    4. \(- 2 a^{3} + 3 a^{2} - 4 a + 5\)

    Solution


  76. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 4 x^{3} - 2 x^{2} + 3 x - 5\] Which of the following expressions is equivalent to \(f(-a)\)?


    1. \(- 4 a^{3} + 2 a^{2} - 3 a + 5\)
    2. \(- 4 a^{3} - 2 a^{2} - 3 a - 5\)
    3. \(4 a^{3} + 2 a^{2} + 3 a + 5\)
    4. \(4 a^{3} - 2 a^{2} + 3 a - 5\)

    Solution


  77. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 2 x^{3} + 4 x^{2} + 2 x + 3\] Which of the following expressions is equivalent to \(f(-a)\)?


    1. \(- 2 a^{3} + 4 a^{2} + 2 a + 3\)
    2. \(2 a^{3} + 4 a^{2} - 2 a + 3\)
    3. \(2 a^{3} - 4 a^{2} - 2 a - 3\)
    4. \(- 2 a^{3} - 4 a^{2} + 2 a - 3\)

    Solution


  78. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 2 x^{3} - 3 x^{2} + 5 x - 4\] Which of the following expressions is equivalent to \(f(-a)\)?


    1. \(- 2 a^{3} + 3 a^{2} - 5 a + 4\)
    2. \(- 2 a^{3} - 3 a^{2} - 5 a - 4\)
    3. \(2 a^{3} + 3 a^{2} + 5 a + 4\)
    4. \(2 a^{3} - 3 a^{2} + 5 a - 4\)

    Solution


  79. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 4 x^{3} + 2 x^{2} + 3 x + 5\] Which of the following expressions is equivalent to \(f(-a)\)?


    1. \(- 4 a^{3} - 2 a^{2} - 3 a - 5\)
    2. \(4 a^{3} - 2 a^{2} + 3 a - 5\)
    3. \(- 4 a^{3} + 2 a^{2} - 3 a + 5\)
    4. \(4 a^{3} + 2 a^{2} + 3 a + 5\)

    Solution


  80. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 3 x^{3} + 5 x^{2} + 4 x - 5\] Which of the following expressions is equivalent to \(f(-a)\)?


    1. \(3 a^{3} + 5 a^{2} + 4 a - 5\)
    2. \(- 3 a^{3} + 5 a^{2} - 4 a - 5\)
    3. \(3 a^{3} - 5 a^{2} + 4 a + 5\)
    4. \(- 3 a^{3} - 5 a^{2} - 4 a + 5\)

    Solution


  81. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 5 x^{3} + 2 x^{2} + 4 x - 3\] Which of the following expressions is equivalent to \(-f(a)\)?


    1. \(5 a^{3} - 2 a^{2} - 4 a + 3\)
    2. \(5 a^{3} + 2 a^{2} - 4 a - 3\)
    3. \(- 5 a^{3} - 2 a^{2} + 4 a + 3\)
    4. \(- 5 a^{3} + 2 a^{2} + 4 a - 3\)

    Solution


  82. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 5 x^{3} + 2 x^{2} + 3 x - 2\] Which of the following expressions is equivalent to \(-f(a)\)?


    1. \(5 a^{3} - 2 a^{2} + 3 a + 2\)
    2. \(- 5 a^{3} - 2 a^{2} - 3 a + 2\)
    3. \(- 5 a^{3} + 2 a^{2} - 3 a - 2\)
    4. \(5 a^{3} + 2 a^{2} + 3 a - 2\)

    Solution


  83. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 5 x^{3} - 4 x^{2} - 5 x - 3\] Which of the following expressions is equivalent to \(-f(a)\)?


    1. \(5 a^{3} - 4 a^{2} - 5 a - 3\)
    2. \(- 5 a^{3} + 4 a^{2} + 5 a + 3\)
    3. \(- 5 a^{3} - 4 a^{2} + 5 a - 3\)
    4. \(5 a^{3} + 4 a^{2} - 5 a + 3\)

    Solution


  84. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 4 x^{3} + 2 x^{2} - 5 x - 3\] Which of the following expressions is equivalent to \(-f(a)\)?


    1. \(- 4 a^{3} - 2 a^{2} - 5 a + 3\)
    2. \(4 a^{3} + 2 a^{2} + 5 a - 3\)
    3. \(4 a^{3} - 2 a^{2} + 5 a + 3\)
    4. \(- 4 a^{3} + 2 a^{2} - 5 a - 3\)

    Solution


  85. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 3 x^{3} + 5 x^{2} - 3 x - 4\] Which of the following expressions is equivalent to \(-f(a)\)?


    1. \(3 a^{3} + 5 a^{2} - 3 a - 4\)
    2. \(- 3 a^{3} + 5 a^{2} + 3 a - 4\)
    3. \(3 a^{3} - 5 a^{2} - 3 a + 4\)
    4. \(- 3 a^{3} - 5 a^{2} + 3 a + 4\)

    Solution


  86. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 5 x^{3} + 3 x^{2} - 5 x + 4\] Which of the following expressions is equivalent to \(-f(a)\)?


    1. \(5 a^{3} + 3 a^{2} - 5 a + 4\)
    2. \(- 5 a^{3} - 3 a^{2} + 5 a - 4\)
    3. \(5 a^{3} - 3 a^{2} - 5 a - 4\)
    4. \(- 5 a^{3} + 3 a^{2} + 5 a + 4\)

    Solution


  87. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 4 x^{3} + 2 x^{2} - 3 x + 4\] Which of the following expressions is equivalent to \(-f(a)\)?


    1. \(- 4 a^{3} - 2 a^{2} - 3 a - 4\)
    2. \(4 a^{3} - 2 a^{2} + 3 a - 4\)
    3. \(- 4 a^{3} + 2 a^{2} - 3 a + 4\)
    4. \(4 a^{3} + 2 a^{2} + 3 a + 4\)

    Solution


  88. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 3 x^{3} - 5 x^{2} + 5 x + 2\] Which of the following expressions is equivalent to \(-f(a)\)?


    1. \(3 a^{3} - 5 a^{2} + 5 a + 2\)
    2. \(3 a^{3} + 5 a^{2} + 5 a - 2\)
    3. \(- 3 a^{3} + 5 a^{2} - 5 a - 2\)
    4. \(- 3 a^{3} - 5 a^{2} - 5 a + 2\)

    Solution


  89. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 3 x^{3} - 3 x^{2} - 2 x + 4\] Which of the following expressions is equivalent to \(-f(a)\)?


    1. \(3 a^{3} + 3 a^{2} - 2 a - 4\)
    2. \(- 3 a^{3} - 3 a^{2} + 2 a + 4\)
    3. \(3 a^{3} - 3 a^{2} - 2 a + 4\)
    4. \(- 3 a^{3} + 3 a^{2} + 2 a - 4\)

    Solution


  90. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 4 x^{3} - 4 x^{2} + 5 x + 2\] Which of the following expressions is equivalent to \(-f(a)\)?


    1. \(4 a^{3} - 4 a^{2} + 5 a + 2\)
    2. \(- 4 a^{3} - 4 a^{2} - 5 a + 2\)
    3. \(4 a^{3} + 4 a^{2} + 5 a - 2\)
    4. \(- 4 a^{3} + 4 a^{2} - 5 a - 2\)

    Solution


  91. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 4 x^{3} - 5 x^{2} + 2 x + 5\] Simplify \(f(-x)\).

    Answer: \(x^3\) \(x^2\) \(x\)



    Solution


  92. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 3 x^{3} + 3 x^{2} + 5 x + 2\] Simplify \(-f(x)\).

    Answer: \(x^3\) \(x^2\) \(x\)



    Solution


  93. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 2 x^{3} + 5 x^{2} + 4 x - 4\] Simplify \(-f(x)\).

    Answer: \(x^3\) \(x^2\) \(x\)



    Solution


  94. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 4 x^{3} - 3 x^{2} - 5 x + 5\] Simplify \(-f(x)\).

    Answer: \(x^3\) \(x^2\) \(x\)



    Solution


  95. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 4 x^{3} + 3 x^{2} - 3 x - 5\] Simplify \(-f(x)\).

    Answer: \(x^3\) \(x^2\) \(x\)



    Solution


  96. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 3 x^{3} + 3 x^{2} - 5 x + 2\] Simplify \(-f(x)\).

    Answer: \(x^3\) \(x^2\) \(x\)



    Solution


  97. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 2 x^{3} - 3 x^{2} + 5 x - 2\] Simplify \(f(-x)\).

    Answer: \(x^3\) \(x^2\) \(x\)



    Solution


  98. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 3 x^{3} - 3 x^{2} + 2 x - 5\] Simplify \(-f(x)\).

    Answer: \(x^3\) \(x^2\) \(x\)



    Solution


  99. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 3 x^{3} - 5 x^{2} - 2 x + 2\] Simplify \(f(-x)\).

    Answer: \(x^3\) \(x^2\) \(x\)



    Solution


  100. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 2 x^{3} - 3 x^{2} + 3 x - 4\] Simplify \(-f(x)\).

    Answer: \(x^3\) \(x^2\) \(x\)



    Solution


  101. Question

    This question is in regards to even and odd functions.

    Let function \(f\) be defined as follows: \[f(x) ~=~ 4 - 3 x^{3}\] Is the function even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  102. Question

    This question is in regards to even and odd functions.

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 2 x^{2} - 4\] Is the function even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  103. Question

    This question is in regards to even and odd functions.

    Let function \(f\) be defined as follows: \[f(x) ~=~ 5 - 5 x^{2}\] Is the function even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  104. Question

    This question is in regards to even and odd functions.

    Let function \(f\) be defined as follows: \[f(x) ~=~ 4 x^{2} - 4 x\] Is the function even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  105. Question

    This question is in regards to even and odd functions.

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 3 x^{3} + 4 x\] Is the function even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  106. Question

    This question is in regards to even and odd functions.

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 3 x^{3} - 4 x\] Is the function even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  107. Question

    This question is in regards to even and odd functions.

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 3 x^{3} - 4 x\] Is the function even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  108. Question

    This question is in regards to even and odd functions.

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 2 x^{2} - 4\] Is the function even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  109. Question

    This question is in regards to even and odd functions.

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 5 x^{3} + 4 x\] Is the function even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  110. Question

    This question is in regards to even and odd functions.

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 5 x^{2} - 3\] Is the function even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  111. Question

    This question is in regards to even and odd functions.

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Is the function’s graph consistent with the function being even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  112. Question

    This question is in regards to even and odd functions.

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Is the function’s graph consistent with the function being even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  113. Question

    This question is in regards to even and odd functions.

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Is the function’s graph consistent with the function being even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  114. Question

    This question is in regards to even and odd functions.

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Is the function’s graph consistent with the function being even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  115. Question

    This question is in regards to even and odd functions.

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Is the function’s graph consistent with the function being even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  116. Question

    This question is in regards to even and odd functions.

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Is the function’s graph consistent with the function being even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  117. Question

    This question is in regards to even and odd functions.

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Is the function’s graph consistent with the function being even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  118. Question

    This question is in regards to even and odd functions.

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Is the function’s graph consistent with the function being even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  119. Question

    This question is in regards to even and odd functions.

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Is the function’s graph consistent with the function being even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  120. Question

    This question is in regards to even and odd functions.

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Is the function’s graph consistent with the function being even, odd, or neither?


    1. Even
    2. Odd
    3. Neither

    Solution


  121. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.

    Express your answer using interval notation.

    What is the domain? [, ]

    What is the range? [, ]



    Solution


  122. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.

    Express your answer using interval notation.

    What is the domain? [, ]

    What is the range? [, ]



    Solution


  123. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.

    Express your answer using interval notation.

    What is the domain? [, ]

    What is the range? [, ]



    Solution


  124. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.

    Express your answer using interval notation.

    What is the domain? [, ]

    What is the range? [, ]



    Solution


  125. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.

    Express your answer using interval notation.

    What is the domain? [, ]

    What is the range? [, ]



    Solution


  126. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.

    Express your answer using interval notation.

    What is the domain? [, ]

    What is the range? [, ]



    Solution


  127. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.

    Express your answer using interval notation.

    What is the domain? [, ]

    What is the range? [, ]



    Solution


  128. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.

    Express your answer using interval notation.

    What is the domain? [, ]

    What is the range? [, ]



    Solution


  129. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.

    Express your answer using interval notation.

    What is the domain? [, ]

    What is the range? [, ]



    Solution


  130. Question

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.

    Express your answer using interval notation.

    What is the domain? [, ]

    What is the range? [, ]



    Solution


  131. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 5 x^{2} - 2 x + 2\] Which of the following expressions is equivalent to \(f(a+h)\)?


    1. \(5 a^{2} - 10 a h + 2 a + 5 h^{2} - 2 h + 2\)
    2. \(5 a^{2} + 10 a h + 2 a + 5 h^{2} + 2 h + 2\)
    3. \(5 a^{2} + 10 a h - 2 a + 5 h^{2} - 2 h + 2\)
    4. \(5 a^{2} - 10 a h - 2 a + 5 h^{2} + 2 h + 2\)

    Solution


  132. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 2 x^{2} - 9 x - 3\] Which of the following expressions is equivalent to \(f(a+h)\)?


    1. \(2 a^{2} - 4 a h - 9 a + 2 h^{2} + 9 h - 3\)
    2. \(2 a^{2} - 4 a h + 9 a + 2 h^{2} - 9 h - 3\)
    3. \(2 a^{2} + 4 a h - 9 a + 2 h^{2} - 9 h - 3\)
    4. \(2 a^{2} + 4 a h + 9 a + 2 h^{2} + 9 h - 3\)

    Solution


  133. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 2 x^{2} + 5 x - 9\] Which of the following expressions is equivalent to \(f(a+h)\)?


    1. \(2 a^{2} - 4 a h - 5 a + 2 h^{2} + 5 h - 9\)
    2. \(2 a^{2} + 4 a h - 5 a + 2 h^{2} - 5 h - 9\)
    3. \(2 a^{2} - 4 a h + 5 a + 2 h^{2} - 5 h - 9\)
    4. \(2 a^{2} + 4 a h + 5 a + 2 h^{2} + 5 h - 9\)

    Solution


  134. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 3 x^{2} + 4 x - 3\] Which of the following expressions is equivalent to \(f(a+h)\)?


    1. \(3 a^{2} + 6 a h + 4 a + 3 h^{2} + 4 h - 3\)
    2. \(3 a^{2} - 6 a h + 4 a + 3 h^{2} - 4 h - 3\)
    3. \(3 a^{2} + 6 a h - 4 a + 3 h^{2} - 4 h - 3\)
    4. \(3 a^{2} - 6 a h - 4 a + 3 h^{2} + 4 h - 3\)

    Solution


  135. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 4 x^{2} - 2 x + 5\] Which of the following expressions is equivalent to \(f(a+h)\)?


    1. \(4 a^{2} + 8 a h - 2 a + 4 h^{2} - 2 h + 5\)
    2. \(4 a^{2} + 8 a h + 2 a + 4 h^{2} + 2 h + 5\)
    3. \(4 a^{2} - 8 a h + 2 a + 4 h^{2} - 2 h + 5\)
    4. \(4 a^{2} - 8 a h - 2 a + 4 h^{2} + 2 h + 5\)

    Solution


  136. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 5 x^{2} + 4 x - 9\] Which of the following expressions is equivalent to \(f(a+h)\)?


    1. \(5 a^{2} - 10 a h - 4 a + 5 h^{2} + 4 h - 9\)
    2. \(5 a^{2} + 10 a h - 4 a + 5 h^{2} - 4 h - 9\)
    3. \(5 a^{2} - 10 a h + 4 a + 5 h^{2} - 4 h - 9\)
    4. \(5 a^{2} + 10 a h + 4 a + 5 h^{2} + 4 h - 9\)

    Solution


  137. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 9 x^{2} - 2 x + 5\] Which of the following expressions is equivalent to \(f(a+h)\)?


    1. \(- 9 a^{2} + 18 a h + 2 a - 9 h^{2} - 2 h + 5\)
    2. \(- 9 a^{2} - 18 a h - 2 a - 9 h^{2} - 2 h + 5\)
    3. \(- 9 a^{2} - 18 a h + 2 a - 9 h^{2} + 2 h + 5\)
    4. \(- 9 a^{2} + 18 a h - 2 a - 9 h^{2} + 2 h + 5\)

    Solution


  138. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 3 x^{2} - 2 x - 9\] Which of the following expressions is equivalent to \(f(a+h)\)?


    1. \(- 3 a^{2} - 6 a h + 2 a - 3 h^{2} + 2 h - 9\)
    2. \(- 3 a^{2} + 6 a h + 2 a - 3 h^{2} - 2 h - 9\)
    3. \(- 3 a^{2} + 6 a h - 2 a - 3 h^{2} + 2 h - 9\)
    4. \(- 3 a^{2} - 6 a h - 2 a - 3 h^{2} - 2 h - 9\)

    Solution


  139. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ 2 x^{2} - 3 x + 3\] Which of the following expressions is equivalent to \(f(a+h)\)?


    1. \(2 a^{2} + 4 a h + 3 a + 2 h^{2} + 3 h + 3\)
    2. \(2 a^{2} - 4 a h - 3 a + 2 h^{2} + 3 h + 3\)
    3. \(2 a^{2} - 4 a h + 3 a + 2 h^{2} - 3 h + 3\)
    4. \(2 a^{2} + 4 a h - 3 a + 2 h^{2} - 3 h + 3\)

    Solution


  140. Question

    Let function \(f\) be defined as follows: \[f(x) ~=~ - 2 x^{2} - 9 x + 2\] Which of the following expressions is equivalent to \(f(a+h)\)?


    1. \(- 2 a^{2} - 4 a h + 9 a - 2 h^{2} + 9 h + 2\)
    2. \(- 2 a^{2} + 4 a h + 9 a - 2 h^{2} - 9 h + 2\)
    3. \(- 2 a^{2} + 4 a h - 9 a - 2 h^{2} + 9 h + 2\)
    4. \(- 2 a^{2} - 4 a h - 9 a - 2 h^{2} - 9 h + 2\)

    Solution


  141. Question

    This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences: \[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    You can round to the nearest hundredth.


    Solution


  142. Question

    This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences: \[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    You can round to the nearest hundredth.


    Solution


  143. Question

    This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences: \[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    You can round to the nearest hundredth.


    Solution


  144. Question

    This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences: \[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    You can round to the nearest hundredth.


    Solution


  145. Question

    This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences: \[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    You can round to the nearest hundredth.


    Solution


  146. Question

    This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences: \[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    You can round to the nearest hundredth.


    Solution


  147. Question

    This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences: \[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    You can round to the nearest hundredth.


    Solution


  148. Question

    This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences: \[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    You can round to the nearest hundredth.


    Solution


  149. Question

    This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences: \[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    You can round to the nearest hundredth.


    Solution


  150. Question

    This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences: \[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]

    A function \(f\) is graphed below.

    plot of chunk unnamed-chunk-1

    You can round to the nearest hundredth.


    Solution


  151. Question

    We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):

    \[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]

    Let function \(f\) be defined as follows: \[f(x) = - 2 x^{2} - 3 x + 4\] Evaluate the average rate of change of \(f(x)\) at \(a=3\) with a step size \(h=0.01\).

    You can round (or truncate) at the hundredths place.


    Solution


  152. Question

    We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):

    \[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]

    Let function \(f\) be defined as follows: \[f(x) = - 4 x^{2} + 2 x - 2\] Evaluate the average rate of change of \(f(x)\) at \(a=6\) with a step size \(h=0.01\).

    You can round (or truncate) at the hundredths place.


    Solution


  153. Question

    We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):

    \[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]

    Let function \(f\) be defined as follows: \[f(x) = 3 x^{2} - 5 x - 2\] Evaluate the average rate of change of \(f(x)\) at \(a=-2\) with a step size \(h=0.1\).

    You can round (or truncate) at the hundredths place.


    Solution


  154. Question

    We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):

    \[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]

    Let function \(f\) be defined as follows: \[f(x) = - 2 x^{2} - 4 x + 4\] Evaluate the average rate of change of \(f(x)\) at \(a=-2\) with a step size \(h=0.001\).

    You can round (or truncate) at the hundredths place.


    Solution


  155. Question

    We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):

    \[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]

    Let function \(f\) be defined as follows: \[f(x) = - 5 x^{2} - 2 x + 4\] Evaluate the average rate of change of \(f(x)\) at \(a=9\) with a step size \(h=0.1\).

    You can round (or truncate) at the hundredths place.


    Solution


  156. Question

    We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):

    \[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]

    Let function \(f\) be defined as follows: \[f(x) = - 2 x^{2} + 5 x - 4\] Evaluate the average rate of change of \(f(x)\) at \(a=-10\) with a step size \(h=0.001\).

    You can round (or truncate) at the hundredths place.


    Solution


  157. Question

    We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):

    \[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]

    Let function \(f\) be defined as follows: \[f(x) = 2 x^{2} + 5 x - 3\] Evaluate the average rate of change of \(f(x)\) at \(a=9\) with a step size \(h=0.01\).

    You can round (or truncate) at the hundredths place.


    Solution


  158. Question

    We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):

    \[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]

    Let function \(f\) be defined as follows: \[f(x) = - 5 x^{2} - 4 x - 3\] Evaluate the average rate of change of \(f(x)\) at \(a=-2\) with a step size \(h=0.001\).

    You can round (or truncate) at the hundredths place.


    Solution


  159. Question

    We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):

    \[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]

    Let function \(f\) be defined as follows: \[f(x) = - 5 x^{2} + 4 x - 3\] Evaluate the average rate of change of \(f(x)\) at \(a=5\) with a step size \(h=0.01\).

    You can round (or truncate) at the hundredths place.


    Solution


  160. Question

    We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):

    \[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]

    Let function \(f\) be defined as follows: \[f(x) = - 3 x^{2} - 5 x - 2\] Evaluate the average rate of change of \(f(x)\) at \(a=0\) with a step size \(h=0.001\).

    You can round (or truncate) at the hundredths place.


    Solution